Ferrite-FEM/Ferrite.jl

Sum factorization techniques for tensor-product elements

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#389 opened on Oct 12, 2021

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Description

Assembly performance of tensor-product elements (we currently just have Lagrange polynomials on RefCube's) can be improved via tensor-product assembly. Thic technique is often called sum-factorization (e.g. [1-2]). Here we rearrange the summation when building the local stiffness matrix. Technically we can also do this on simplices, see e.g. [3].

TODO here is to provide an example and maybe make internal modifications if required. This technique is not too important for low-order basis functions, because it primarily decreases the evaluation complexity.

References

[1] Homolya, M., Kirby, R. C., & Ham, D. A. (2017). Exposing and exploiting structure: optimal code generation for high-order finite element methods. arXiv preprint arXiv:1711.02473.

[2] Kronbichler, M., & Kormann, K. (2012). A generic interface for parallel cell-based finite element operator application. Computers & Fluids, 63, 135-147.

[3] Eibner, T., & Melenk, J. M. (2005). Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison. SFB 393.

Contributor guide

Research direction
Read the referenced papers to understand sum factorization technique, then identify where tensor product assembly can be applied in the Ferrite codebase and create an example.
Tech stack
None
Domain
backend
Issue type
Feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-2 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
Active
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
Needs investigation
Prerequisites
Finite element methods
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
50